Adiabatic quantum games and phase-transition-like behavior between optimal strategies

• Autor(a) principal: de Ponte, M. A. [UNESP]
• Data de Publicação: 2018
• Outros Autores: Santos, Alan C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s11128-018-1918-6; http://hdl.handle.net/11449/176314
• topic: Adiabatic evolution; Phase-transition-like behavior; Quantum games

In this paper we propose a game of a single qubit whose strategies can be implemented adiabatically. In addition, we show how to implement the strategies of a quantum game through controlled adiabatic evolutions, where we analyze the payment of a quantum player for various situations of interest: (1) when the players receive distinct payments, (2) when the initial state is an arbitrary superposition, and (3) when the device that implements the strategy is inefficient. Through a graphical analysis, it is possible to notice that the curves that represent the gains of the players present a behavior similar to the curves that give rise to a phase transition in thermodynamics. These transitions are associated with optimal strategy changes and occur in the absence of entanglement and interaction between the players.